In general, is it kosher to use a z-score as a dependent variable in a
linear regression? Is it "better" to use some sort of ratio
measurement?

Keep in mind that if you say

regress y x1 x2, beta

you are in effect running an OLS of z-scored y on z-scored x1 and z-
scored x2.

Kit

As Austin noted, it is not clear to me that this is the kind of
z-score the original poster had in mind. It sounded like z scores
were being computed on an individual by individual basis.

Incidentally, if you install -spost9- from J. Scott Long's personal
site, the command -listcoef- lets you do y-standardization,
x-standardization, and xy-standardization. So if, say, you just
wanted the y's standardized but not the x's, you could run -listcoef-
after the regress command. Example: